It is conventional in the automotive industry to apply a soap or lubricant composition to the rim of a wheel to facilitate the mounting of a tire on the wheel. Various machines have been developed for soaping wheel rims on a mass production basis, however, for true mass production line use, the soaper must be able to handle several different models or sizes of wheels whose outside diameter, axial width, and center hole diameter will differ from each other over ranges as large as 4 or 5 inches. A set of standard steel wheels for an economy car may be followed through the soaper by a set of optional solid aluminum wheels of substantially greater axial width. This procedure does not allow for any adjustment or resetting of the wheel engaging parts of the soaper to accommodate for dimensional differences and the soaper must thus be capable of accepting and handling wheels having outside diameters, axial widths and central hole openings falling anywhere within pre-selected dimensional ranges. The problems associated with wheel soaping and tire soaping have been considered in the prior art, see for example U.S. Pat. No. 4,723,563; U.S. Pat. No. 4,843,159; and U.S. Pat. No. 5,642,790.